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arXiv · 2101.03199

Global Solutions of the Nernst-Planck-Euler Equations

Mihaela Ignatova·Jingyang Shu
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Abstract

We consider the initial value problem for the Nernst-Planck equations coupled to the incompressible Euler equations in $\mathbb T^2$. We prove global existence of weak solutions for vorticity in $L^p$. We also obtain global existence and uniqueness of smooth solutions. We show that smooth solutions of the Nernst-Planck-Navier-Stokes equations converge to solutions of the Nernst-Planck-Euler equations as viscosity tends to zero. All the results hold for large data.

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Mihaela Ignatova, Jingyang Shu. 2021-01-08. Global Solutions of the Nernst-Planck-Euler Equations. https://arxiv.org/abs/2101.03199

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